TY - JOUR

T1 - Application of the full Bayesian significance test to model selection under informative sampling

AU - Sikov, A.

AU - Stern, J. M.

N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

PY - 2019/2/15

Y1 - 2019/2/15

N2 - Adopting likelihood based methods of inference in the case of informative sampling often presents a number of difficulties, particularly, if the parametric form of the model that describes the sample selection mechanism is unknown, and thus requires application of some model selection approach. These difficulties generally arise either due to complexity of the model holding in the sample, or due to identifiability problems. As a remedy we propose alternative approach to model selection and estimation in the case of informative sampling. Our approach is based on weighted estimation equations, where the contribution to the estimation equation from each observation is weighted by the inverse probability of being selected. We show how weighted estimation equations can be incorporated in a Bayesian analysis, and how the full Bayesian significance test can be implemented as a model selection tool. We illustrate the efficiency of the proposed methodology by a simulation study.

AB - Adopting likelihood based methods of inference in the case of informative sampling often presents a number of difficulties, particularly, if the parametric form of the model that describes the sample selection mechanism is unknown, and thus requires application of some model selection approach. These difficulties generally arise either due to complexity of the model holding in the sample, or due to identifiability problems. As a remedy we propose alternative approach to model selection and estimation in the case of informative sampling. Our approach is based on weighted estimation equations, where the contribution to the estimation equation from each observation is weighted by the inverse probability of being selected. We show how weighted estimation equations can be incorporated in a Bayesian analysis, and how the full Bayesian significance test can be implemented as a model selection tool. We illustrate the efficiency of the proposed methodology by a simulation study.

KW - Bayesian significance measures

KW - Design variables

KW - Horvitz–Thompson estimator

KW - Inclusion probability

KW - Informative sampling

KW - Population distribution

KW - Sample distribution

UR - http://www.scopus.com/inward/record.url?scp=84986309935&partnerID=8YFLogxK

U2 - 10.1007/s00362-016-0828-x

DO - 10.1007/s00362-016-0828-x

M3 - Article

AN - SCOPUS:84986309935

SN - 0932-5026

VL - 60

SP - 89

EP - 104

JO - Statistical Papers

JF - Statistical Papers

IS - 1

ER -